Browsing by Author "Shieh, Gwowen"

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A comparative appraisal of two equivalence tests for multiple standardized effects
(2016-04)
Shieh, Gwowen
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管理科學系
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Department of Management Science
Equivalence testing is recommended as a better alternative to the traditional difference based methods for demonstrating the comparability of two or more treatment effects. Although equivalent tests of two groups are widely discussed, the natural extensions for assessing equivalence between several groups have not been well examined. This article provides a detailed and schematic comparison of the ANOVA F and the studentized range tests for evaluating the comparability of several standardized effects. Power and sample size appraisals of the two grossly distinct approaches are conducted in terms of a constraint on the range of the standardized means when the standard deviation of the standardized means is fixed. Although neither method is uniformly more powerful, the studentized range test has a clear advantage in sample size requirements necessary to achieve a given power when the underlying effect configurations are close to the priori minimum difference for determining equivalence. For actual application of equivalence tests and advance planning of equivalence studies, both SAS and R computer codes are available as supplementary files to implement the calculations of critical values, p-values, power levels, and sample sizes. (C) 2015 Elsevier Ireland Ltd. All rights reserved.
A comparison of two indices for the intraclass correlation coefficient
(2012-12-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
In the present study, we examined the behavior of two indices for measuring the intraclass correlation in the one-way random effects model: the prevailing ICC(1) (Fisher, 1938) and the corrected eta-squared (Bliese & Halverson, 1998). These two procedures differ both in their methods of estimating the variance components that define the intraclass correlation coefficient and in their performance of bias and mean squared error in the estimation of the intraclass correlation coefficient. In contrast with the natural unbiased principle used to construct ICC(1), in the present study it was analytically shown that the corrected eta-squared estimator is identical to the maximum likelihood estimator and the pairwise estimator under equal group sizes. Moreover, the empirical results obtained from the present Monte Carlo simulation study across various group structures revealed the mutual dominance relationship between their truncated versions for negative values. The corrected eta-squared estimator performs better than the ICC(1) estimator when the underlying population intraclass correlation coefficient is small. Conversely, ICC(1) has a clear advantage over the corrected eta-squared for medium and large magnitudes of population intraclass correlation coefficient. The conceptual description and numerical investigation provide guidelines to help researchers choose between the two indices for more accurate reliability analysis in multilevel research.
A systematic approach to designing statistically powerful heteroscedastic 2 x 2 factorial studies while minimizing financial costs
(2016-08-31)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
Background: The 2 x 2 factorial design is widely used for assessing the existence of interaction and the extent of generalizability of two factors where each factor had only two levels. Accordingly, research problems associated with the main effects and interaction effects can be analyzed with the selected linear contrasts. Methods: To correct for the potential heterogeneity of variance structure, the Welch-Satterthwaite test is commonly used as an alternative to the t test for detecting the substantive significance of a linear combination of mean effects. This study concerns the optimal allocation of group sizes for the Welch-Satterthwaite test in order to minimize the total cost while maintaining adequate power. The existing method suggests that the optimal ratio of sample sizes is proportional to the ratio of the population standard deviations divided by the square root of the ratio of the unit sampling costs. Instead, a systematic approach using optimization technique and screening search is presented to find the optimal solution. Results: Numerical assessments revealed that the current allocation scheme generally does not give the optimal solution. Alternatively, the suggested approaches to power and sample size calculations give accurate and superior results under various treatment and cost configurations. Conclusions: The proposed approach improves upon the current method in both its methodological soundness and overall performance. Supplementary algorithms are also developed to aid the usefulness and implementation of the recommended technique in planning 2 x 2 factorial designs.
A unified approach to power calculation and sample size determination for random regression models
(2007-09-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all variables having a joint multivariate normal distribution. This paper presents a unified approach to determining power and sample size for random regression models with arbitrary distribution configurations for explanatory variables. Numerical examples are provided to illustrate the usefulness of the proposed method and Monte Carlo simulation studies are also conducted to assess the accuracy. The results show that the proposed method performs well for various model specifications and explanatory variable distributions.
Appraising Minimum Effect of Standardized Contrasts in ANCOVA Designs: Statistical Power, Sample Size, and Covariate Imbalance Considerations
(1970-01-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
The concepts and implementation of standardized mean differences and minimum effect tests have been emphasized in ANOVA. The corresponding processes and implications are, however, not yet well explicated in the context of ANCOVA. To enhance the usefulness of ANCOVA, this article describes the minimum effect tests of standardized contrast as a valuable alternative to the hypothesis testing of no effect difference and the conventional evaluation of unstandardized effects in ANCOVA. Power and sample size procedures are developed to accommodate covariate randomness and imbalance for randomized and nonrandomized designs. The data from a clinical study of comparing two treatments for gingivitis are used to illustrate the application of the suggested approaches. The emphases of numerical appraisal are on the merit of minimum effect detection in comparative analysis and the influence of covariate feature in power and sample size computation. The proposed power and sample size calculations improve upon approximate formulas by fully accounting for the stochastic property and intrinsic disparity of the covariate variables. Computer algorithms are available for calculating thep-value, power level, and sample size of one- and two-sided minimum effect tests.
Assessing Agreement Between Two Methods of Quantitative Measurements: Exact Test Procedure and Sample Size Calculation
(1970-01-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
Assessment of agreement between measurement methods is an important problem in medical practice and research. Several two one-sided tests (TOST) procedures have been proposed to evaluate whether two methods have sufficient agreement. These TOST techniques of limits of agreement or normal percentiles are natural generalizations of the favorable TOST procedure of mean differences. But their fundamental behavior of Type I error control has not been examined. This article describes an improved and exact approach for declaring agreement between two measurement methods when the range of central proportion of paired differences is within the designated threshold interval around zero. Theoretical examinations and numerical investigations are provided to justify the advantages of the proposed approach and to illustrate the shortcomings of the existing TOST procedures for assessing agreement between two methods. To facilitate the suggested agreement appraisal in design planning, the corresponding power and sample size formulas are also derived. Both SAS and R algorithms are presented for conducting agreement test, power calculation, and sample size determination in method comparison studies.
Choosing the best index for the average score intraclass correlation coefficient
(2016-09)
Shieh, Gwowen
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管理科學系
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Department of Management Science
The intraclass correlation coefficient (ICC)(2) index from a one-way random effects model is widely used to describe the reliability of mean ratings in behavioral, educational, and psychological research. Despite its apparent utility, the essential property of ICC(2) as a point estimator of the average score intraclass correlation coefficient is seldom mentioned. This article considers several potential measures and compares their performance with ICC(2). Analytical derivations and numerical examinations are presented to assess the bias and mean square error of the alternative estimators. The results suggest that more advantageous indices can be recommended over ICC(2) for their theoretical implication and computational ease.
Clarifying the role of mean centring in multicollinearity of interaction effects
(2011-11-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
Moderated multiple regression (MMR) is frequently employed to analyse interaction effects between continuous predictor variables. The procedure of mean centring is commonly recommended to mitigate the potential threat of multicollinearity between predictor variables and the constructed cross-product term. Also, centring does typically provide more straightforward interpretation of the lower-order terms. This paper attempts to clarify two methodological issues of potential confusion. First, the positive and negative effects of mean centring on multicollinearity diagnostics are explored. It is illustrated that the mean centring method is, depending on the characteristics of the data, capable of either increasing or decreasing various measures of multicollinearity. Second, the exact reason why mean centring does not affect the detection of interaction effects is given. The explication shows the symmetrical influence of mean centring on the corrected sum of squares and variance inflation factor of the product variable while maintaining the equivalence between the two residual sums of squares for the regression of the product term on the two predictor variables. Thus the resulting test statistic remains unchanged regardless of the obvious modification of multicollinearity with mean centring. These findings provide a clear understanding and demonstration on the diverse impact of mean centring in MMR applications.
Comparison of alternative approaches for difference, noninferiority, and equivalence testing of normal percentiles
(2020-03-13)
Shieh, Gwowen
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管理科學系
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Department of Management Science
Background Percentiles are widely used in scientific research for determining the comparative magnitude and reference limit of quantitative measurements. The investigations for point and interval estimation of normal percentiles are well documented in the literature. However, the corresponding statistical tests of hypothesis have received relatively little attention. Methods To facilitate data analysis and design planning of percentile study, this paper aims to present hypothesis testing procedures and associated power functions for assessing the difference, noninferiority, and equivalence of normal percentiles. Results Numerical illustrations about drug dissolution are provided to demonstrate the usefulness of the suggested exact approaches and the deficiency of approximate methods. Conclusions The exact approaches are superior to the approximate methods on the basis of control of Type I errors. Computer algorithms are constructed to implement the recommended test procedures and sample size calculations for percentile analysis.
Confidence intervals and sample size calculations for the weighted eta-squared effect sizes in one-way heteroscedastic ANOVA
(2013-03-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
Effect size reporting and interpreting practices have been extensively recommended in academic journals when primary outcomes of all empirical studies have been analyzed. This article presents an alternative approach to constructing confidence intervals of the weighted eta-squared effect size within the context of one-way heteroscedastic ANOVA models. It is shown that the proposed interval procedure has advantages over an existing method in its theoretical justification, computational simplicity, and numerical performance. For design planning, the corresponding sample size procedures for precise interval estimation of the weighted eta-squared association measure are also delineated. Specifically, the developed formulas compute the necessary sample sizes with respect to the considerations of expected confidence interval width and tolerance probability of interval width within a designated value. Supplementary computer programs are provided to aid the implementation of the suggested techniques in practical applications of ANOVA designs when the assumption of homogeneous variances is not tenable.
Detecting Interaction Effects in Moderated Multiple Regression With Continuous Variables Power and Sample Size Considerations
(2009-07-01)
Shieh, Gwowen
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交大名義發表
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National Chiao Tung University
In view of the long-recognized difficulties in detecting interactions among continuous variables in moderated multiple regression analysis, this article aims to address the problem by providing feasible solutions to power calculation and sample size determination for significance test of moderating effects. The proposed approach incorporates the essential factors of strength of moderator effect, magnitude of error variation, and distributional property of predictor and moderator variables into a unified framework. Accordingly, careful consideration across different plausible and practical configurations of the prescribed factors is an important aspect of power and sample size computations in planning moderated multiple regression research. The performance of the suggested procedure and an alternative simplified method is illustrated with detailed numerical studies. The simulation results demonstrate that an acceptable degree of accuracy can be obtained using the recommended method in assessing moderated relationships.
Detection of interactions between a dichotomous moderator and a continuous predictor in moderated multiple regression with heterogeneous error variance
(2009-02-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
Moderated multiple regression (MMR) has been widely used to investigate the interaction or moderating effects of a categorical moderator across a variety of subdisciplines in the behavioral and social sciences. In view of the frequent violation of the homogeneity of error variance assumption in MMR applications, the weighted least squares (WLS) approach has been proposed as one of the alternatives to the ordinary least squares method for the detection of the interaction effect between a dichotomous moderator and a continuous predictor. Although the existing result is informative in assuring the statistical accuracy and computational ease of the WLS-based method, no explicit algebraic formulation and underlying distributional details are available. This article aims to delineate the fundamental properties of the WLS test in connection with the well-known Welch procedure for regression slope homogeneity under error variance heterogeneity. With elaborately systematic derivation and analytic assessment, it is shown that the notion of WLS is implicitly embedded in the Welch approach. More importantly, extensive simulation study is conducted to demonstrate the conditions in which the Welch test will substantially outperform the WLS method; they may yield different conclusions. Welch's solution to the Behrens-Fisher problem is so entrenched that the use of its direct extension within the linear regression framework can arguably be recommended. In order to facilitate the application of Welch's procedure, the SAS and R computing algorithms are presented. The study contributes to the understanding of methodological variants for detecting the effect of a dichotomous moderator in the context of moderated multiple regression. Supplemental materials for this article may be downloaded from brm.psychonomic-joumals.org/content/supplemental.
Determining Sample Size With a Given Range of Mean Effects in One-Way Heteroscedastic Analysis of Variance
(2013-07-03)
Shieh, Gwowen
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Jan, Show-Li
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交大名義發表
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管理科學系
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National Chiao Tung University
The authors examined 2 approaches for determining the required sample size of Welch's test for detecting equality of means when the greatest difference between any 2 group means is given. It is shown that the actual power obtained with the sample size of the suggested approach is consistently at least as great as the nominal power. However, the sample size given by the method of Guo and Luh (2008) does not always guarantee the minimum power performance. Furthermore, the computed sample size and associated power of their formula tend to be larger than those provided with the proposed procedure. A supplementary computer program is provided to aid the implementation of the proposed technique in planning analysis of variance designs.
Determining Sample Sizes for Precise Contrast Analysis With Heterogeneous Variances
(2014-04-01)
Jan, Show-Li
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Shieh, Gwowen
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交大名義發表
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National Chiao Tung University
The analysis of variance (ANOVA) is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study examines the sample size procedures for precise interval estimation of linear contrasts within the context of one-way heteroscedastic ANOVA models. The desired precision of both individual and simultaneous confidence intervals is evaluated with respect to the control of expected half width and to the tolerance probability of interval half width within a designated value. Supplementary computer programs are developed to aid the usefulness and implementation of the proposed techniques. The suggested sample size procedures improve upon the existing approaches and extend the methodology development in the statistical literature.
Effect size, statistical power, and sample size for assessing interactions between categorical and continuous variables
(2019-02-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
The reporting and interpretation of effect size estimates are widely advocated in many academic journals of psychology and related disciplines. However, such concern has not been adequately addressed for analyses involving interactions between categorical and continuous variables. For the purpose of improving current practice, this article presents fundamental features and theoretical developments for the variance of standardized slopes as a desirable standardized effect size measure for the degree of disparity between several slope coefficients. To estimate the effect size, a consistent and nearly unbiased estimator is described and a simple refinement is emphasized for extreme situations whenever appropriate. The essential problems of power and sample size calculations for testing the equality of slope coefficients are also considered. According to the analytic justification and empirical assessment, the exact approach has a clear advantage over the approximate methods. Both SAS and R computer codes are provided to facilitate practical accessibility of the proposed techniques in interaction studies.
Estimation of the simple correlation coefficient
(2010-11-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
This article investigates some unfamiliar properties of the Pearson product-moment correlation coefficient for the estimation of simple correlation coefficient. Although Pearson's r is biased, except for limited situations, and the minimum variance unbiased estimator has been proposed in the literature, researchers routinely employ the sample correlation coefficient in their practical applications, because of its simplicity and popularity. In order to support such practice, this study examines the mean squared errors of r and several prominent formulas. The results reveal specific situations in which the sample correlation coefficient performs better than the unbiased and nearly unbiased estimators, facilitating recommendation of r as an effect size index for the strength of linear association between two variables. In addition, related issues of estimating the squared simple correlation coefficient are also considered.
Exact Analysis of Squared Cross-Validity Coefficient in Predictive Regression Models
(2009)
Shieh, Gwowen
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管理科學系
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Department of Management Science
In regression analysis, the notion of population validity is of theoretical interest for describing the usefulness of the underlying regression model, whereas the presumably more important concept of population cross-validity represents the predictive effectiveness for the regression equation in future research. It appears that the inference procedures of the squared multiple correlation coefficient have been extensively developed. In contrast, a full range of statistical methods for the analysis of the squared cross-validity coefficient is considerably far from complete. This article considers a distinct expression for the definition of the squared cross-validity coefficient as the direct connection and monotone transformation to the squared multiple correlation coefficient. Therefore, all the currently available exact methods for interval estimation, power calculation, and sample size determination of the squared multiple correlation coefficient are naturally modified and extended to the analysis of the squared cross-validity coefficient. The adequacies of the existing approximate procedures and the suggested exact method are evaluated through a Monte Carlo study. Furthermore, practical applications in areas of psychology and management are presented to illustrate the essential features of the proposed methodologies. The first empirical example uses 6 control variables related to driver characteristics and traffic congestion and their relation to stress in bus drivers, and the second example relates skills, cognitive performance, and personality to team performance measures. The results in this article can facilitate the recommended practice of cross-validation in psychological and other areas of social science research.
Exact interval estimation, power calculation, and sample size determination in normal correlation analysis
(2006-09-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple correlation coefficients. The inversion principle and monotonicity property of the proposed formulations are used to describe alternative approaches to the exact interval estimation, power calculation, and sample size determination for correlation coefficients.
Exact Power and Sample Size Calculations for the Two One-Sided Tests of Equivalence
(2016-09-06)
Shieh, Gwowen
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管理科學系
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Department of Management Science
Equivalent testing has been strongly recommended for demonstrating the comparability of treatment effects in a wide variety of research fields including medical studies. Although the essential properties of the favorable two one-sided tests of equivalence have been addressed in the literature, the associated power and sample size calculations were illustrated mainly for selecting the most appropriate approximate method. Moreover, conventional power analysis does not consider the allocation restrictions and cost issues of different sample size choices. To extend the practical usefulness of the two one-sided tests procedure, this article describes exact approaches to sample size determinations under various allocation and cost considerations. Because the presented features are not generally available in common software packages, both R and SAS computer codes are presented to implement the suggested power and sample size computations for planning equivalence studies. The exact power function of the TOST procedure is employed to compute optimal sample sizes under four design schemes allowing for different allocation and cost concerns. The proposed power and sample size methodology should be useful for medical sciences to plan equivalence studies.
Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient
(2008-04-01)
Shieh, Gwowen
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管理科學系
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Department of Management Science
The sample squared multiple correlation coefficient is widely used for describing the usefulness of a multiple linear regression model in many areas of science. In this article, the author considers the problem of estimating the squared multiple correlation coefficient and the squared cross-validity coefficient under the assumption that the response and predictor variables have a joint multinormal distribution. Detailed numerical investigations are conducted to assess the exact bias and mean square error of the proposed modifications of established estimators. Notably, the positive-part Pratt estimator and the synthesis of Browne and positive-part Pratt estimators are recommended in the estimation of squared multiple correlation coefficient and squared cross-validity coefficient, respectively, for their overall advantages of incurring the least amount of statistical discrepancy and computational requirement.